Comparing Clustering with Pairwise and Relative Constraints: A Unified Framework

Yuanli Pei, Xiaoli Z. Fern, Teresa Vania Tjahja, Rómer Rosales

Abstract: Clustering can be improved with the help of side information about the similarity relationships among instances. Such information has been commonly represented by two types of constraints: pairwise constraints and relative constraints, regarding similarities about instance pairs and triplets, respectively. Prior work has mostly considered these two types of constraints separately and developed individual algorithms to learn from each type. In practice, however, it is critical to understand/compare the usefulness of the two types of constraints as well as the cost of acquiring them, which has not been studied before. This paper provides an extensive comparison of clustering with these two types of constraints. Specifically, we compare their impacts both on human users that provide such constraints and on the learning system that incorporates such constraints into clustering. In addition, to ensure that the comparison of clustering is performed on equal ground (without the potential bias introduced by different learning algorithms), we propose a probabilistic semi-supervised clustering framework that can learn from either type of constraints. Our experiments demonstrate that the proposed semi-supervised clustering framework is highly effective at utilizing both types of constraints to aid clustering. Our user study provides valuable insights regarding the impact of the constraints on human users, and our experiments on clustering with the human-labeled constraints reveal that relative constraint is often more efficient at improving clustering.